Problem: Solve for $x$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $4x+4\leq9x+8$
$\begin{aligned}4x+4&\leq9x+8 \\\\ 4x&\leq 9x+4 &(\text{Subtract } 4 \text{ from both sides}) \\\\ -5x &\leq 4 &(\text{Subtract } 9x \text{ from both sides})\\\\ 5x&\geq-4&(\text{Multiply both sides by }-1)\\\\ x&\geq-\dfrac{4}{5}&(\text{Divide both sides by }5) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $x \geq -\dfrac{4}{5}$.